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A cumulative sum is a sequence of partial sums of a given sequence. For example, the cumulative sums of the sequence {a,b,c,...}, are a, a+b, a+b+c, .... Cumulative sums are ...

An algorithm which extrapolates the partial sums s_n of a series sum_(n)a_n whose convergence is approximately geometric and accelerates its rate of convergence. The ...

The ordinary Onsager equation is the sixth-order ordinary differential equation (d^3)/(dx^3)[e^x(d^2)/(dx^2)(e^x(dy)/(dx))]=f(x) (Vicelli 1983; Zwillinger 1997, p. 128), ...

Given F_1(x,y,z,u,v,w) = 0 (1) F_2(x,y,z,u,v,w) = 0 (2) F_3(x,y,z,u,v,w) = 0, (3) if the determinantof the Jacobian |JF(u,v,w)|=|(partial(F_1,F_2,F_3))/(partial(u,v,w))|!=0, ...

A relation < is a strict order on a set S if it is 1. Irreflexive: a<a does not hold for any a in S. 2. Asymmetric: if a<b, then b<a does not hold. 3. Transitive: a<b and b<c ...

The partial order width of a set P is equal to the minimum number of chains needed to cover P. Equivalently, if a set P of ab+1 elements is partially ordered, then P contains ...

For the Helmholtz differential equation to be separable in a coordinate system, the scale factors h_i in the Laplacian del ...

An initial value problem is a problem that has its conditions specified at some time t=t_0. Usually, the problem is an ordinary differential equation or a partial ...

In three dimensions, the spherical harmonic differential equation is given by ...

A Bäcklund transformation allows additional solutions to a nonlinear partial differential equations to be found if one particular solution is already known.